Problem: What do the following two equations represent? $3x+3y = 1$ $12x+12y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x+3y = 1$ $3y = -3x+1$ $y = -1x + \dfrac{1}{3}$ Putting the second equation in $y = mx + b$ form gives: $12x+12y = 5$ $12y = -12x+5$ $y = -1x + \dfrac{5}{12}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.